"""Reproduzierbare Winkelpruefung; benoetigt Python 3 und mpmath."""
import mpmath as mp


def examine(dps):
    with mp.workdps(dps):
        phi = (1 + mp.sqrt(5)) / 2
        tolerance = mp.power(10, -(dps - 20))
        sine = {a: mp.sin(mp.pi * a / 180) for a in range(1, 100)}
        cosine = {b: mp.cos(mp.pi * b / 180)
                  for b in range(1, 100) if b != 90}
        matches, golden_pairs = [], []
        checked = 0
        for a in range(1, 100):
            for b, denominator in cosine.items():
                checked += 1
                q = abs(sine[a] / denominator)
                # Im definierten Winkelbereich sind dies genau die |q|=1-Faelle.
                if a + b == 90 or abs(a - b) == 90:
                    q = mp.mpf(1)
                # Vier Anfangsziffern OHNE Rundung; die fuehrende 0 zaehlt mit.
                integer_digits = len(str(int(mp.floor(q))))
                first_four = f"{int(mp.floor(q * mp.power(10, 4 - integer_digits))):04d}"
                input_digits = f"{a:02d}{b:02d}"
                if sorted(first_four) == sorted(input_digits):
                    matches.append(input_digits)
                # Numerischer Vergleich; die drei Identitaeten separat beweisbar.
                if abs(q - 1 / phi) < tolerance:
                    golden_pairs.append(input_digits)
        common = sorted(set(matches) & set(golden_pairs))
        return checked, matches, golden_pairs, common


EXPECTED_MATCHES = "0107 0610 0841 1077 1210 1220 1598 1860 4081 4807 5261 6592 8187 8492 8851 9478".split()
EXPECTED = (9702, EXPECTED_MATCHES, ["1860", "3036", "3618"], ["1860"])

if __name__ == "__main__":
    result_120 = examine(120)
    result_200 = examine(200)
    assert result_120 == result_200 == EXPECTED, "Ergebnisabweichung"
    for precision, result in [(120, result_120), (200, result_200)]:
        checked, matches, golden_pairs, common = result
        print(f"Praezision: {precision} Dezimalstellen; gepruefte Paare: {checked}")
        print(f"Zifferntreffer ({len(matches)}): {' '.join(matches)}")
        print(f"1/Phi-Paare: {' '.join(golden_pairs)}")
        print(f"Gemeinsamer Treffer: {' '.join(common)}")